There is no bump in Cycles
I think it goes like this:
If you set the Cycles settings of a material to 'Displacement' only, then EEVEE, not supporting Displacement shading,  will substitute Bump mapping for any Displacement input to the Material Output node, to make the Cycles and EEVEE renders to look as similar as possible.
Cycles can't depend on that substitution - if you want a normal or bump-map in Cycles, you have to ask for one explicitly:

Not necessarily in Object space, but you get the idea..